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13 Jul 2024, 06:30
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First to answer this question we have to break down 22,25 and 32 into prime divisors
22 = 11*2
25 = 5*5
32 = 2*2*2*2*2
So the number must be divisble by 2*2*2*2*2*2*5*5*11
It is asking for the largest 4-digit number that can be added to 7,700 therefore we can pick the largest number from the answer choices and work our way down.
So we start with 9,900.
(It is worth nothing that each of the answer choices can be written as 11*100*__)
In the case of 9,900 + 7,700, we can write this as 9*11*100 + 7*11*100
We can take 11*100 out of the brackets for 11*100(9+7).
- The 11 remains
- 100 can be broken down into 5*5*2*2
- and 9+7 = 16 which can be written as 2*2*2*2
So 9,900+7,700 = 2*2*2*2*2*2*5*5*11 which can be divisible by 22,25,32
The answer is E
22 = 11*2
25 = 5*5
32 = 2*2*2*2*2
So the number must be divisble by 2*2*2*2*2*2*5*5*11
It is asking for the largest 4-digit number that can be added to 7,700 therefore we can pick the largest number from the answer choices and work our way down.
So we start with 9,900.
(It is worth nothing that each of the answer choices can be written as 11*100*__)
In the case of 9,900 + 7,700, we can write this as 9*11*100 + 7*11*100
We can take 11*100 out of the brackets for 11*100(9+7).
- The 11 remains
- 100 can be broken down into 5*5*2*2
- and 9+7 = 16 which can be written as 2*2*2*2
So 9,900+7,700 = 2*2*2*2*2*2*5*5*11 which can be divisible by 22,25,32
The answer is E
Bunuel
16 Jul 2025, 00:28
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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